Question

How do you solve the system $2x+y=0$ and $3x-y=-10$ by graphing?

Answer 1

Hint: We will find two points that satisfy the first equation. Then we will draw a line passing through these two points. Then we will find two points satisfying the second equation. We will draw a line passing through these two points. Then we will look for the coordinates of the point of intersection of these two lines. The coordinates of the point of intersection of the two lines is the solution.

Complete step by step answer:
The given system of linear equations is
$2x+y=0....(i)$
$3x-y=-10....(ii)$
We will use the graphing method to find the solution of this system of linear equations.
Let us find two points that satisfy the equation $(i)$. If we substitute $x=0$, we get $y=0$. So, the origin is one point on the line represented by the first equation. If we substitute $x=-1$, then we get $y=2$. So, the second point is $\left( -1,2 \right)$. Let us draw the graph of the first equation. The line passes through the points $\left( 0,0 \right)$ and $\left( -1,2 \right)$. The graph looks like the following,
          

Now, let us find two points satisfying the equation $(ii)$. If we substitute $x=0$, we get $y=10$. So, the point $\left( 0,10 \right)$ lies on the line represented by the second equation. If we substitute $x=1$, then we get $y=13$. So, the second point is $\left( 1,13 \right)$. Let us draw the graph of the second equation. The line passes through the points $\left( 0,10 \right)$ and $\left( 1,13 \right)$. The graph looks like the following,
 

We can see from the graph that the point of intersection of the two lines is $\left( -2,4 \right)$. This is the solution of the given system of equations.

Note:
There are other methods of solving a system of linear equations. These methods are method of substitution and method of Gauss elimination. We know that a linear equation represents a line. We also know that only one straight line passes through two distinct points. Therefore, it suffices to find two points that satisfy a linear equation to draw its graph.